Variational existence theory for hydroelastic solitary waves: Une théorie variationnelle d'existence d'ondes solitaires hydroélastiques

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Abstract

This paper presents an existence theory for solitary waves at the interface between a thin ice sheet (modelled using the Cosserat theory of hyperelastic shells) and an ideal fluid (of finite depth and in irrotational motion) for sufficiently large values of a dimensionless parameter γ. We establish the existence of a minimiser of the wave energy E subject to the constraint I=2μ, where I is the horizontal impulse and 0<μ≪1, and show that the solitary waves detected by our variational method converge (after an appropriate rescaling) to solutions to the nonlinear Schrödinger equation with cubic focussing nonlinearity as μ↓0.

Detaljer

Författare
Enheter & grupper
Externa organisationer
  • Loughborough University
  • Saarland University
Forskningsområden

Ämnesklassifikation (UKÄ) – OBLIGATORISK

  • Matematik
Originalspråkengelska
Sidor (från-till)1078-1086
Antal sidor9
TidskriftComptes Rendus Mathematique
Volym354
Utgivningsnummer11
StatusPublished - 2016 nov 1
PublikationskategoriForskning
Peer review utfördJa